The celebrated variational autoencoder (vae) [1]}, [2]} address this concern directly through an explicit likelihood model \(p(\mathbf {x}| \mathbf {z})\)  and a variational approximation of the representation posterior \(p(\mathbf {z}| \mathbf {x})\) . Both these distributions have parameters predicted by neural networks that act similarly to the encoder–decoder pair of the classic autoencoder.
